# Triangle A has sides of lengths 36 ,24 , and 18 . Triangle B is similar to triangle A and has a side of length 5 . What are the possible lengths of the other two sides of triangle B?

May 3, 2016

There are 3 different triangle possible because we do not know which side of the smaller triangle is equal to 5.

#### Explanation:

In similar figures. the sides are in the same ratio. However in this case, we are not told which side of the smaller triangle has a length of 5. There are therefore 3 possibilities.

$\frac{36}{5} = \frac{24}{3 \frac{1}{3}} = \frac{18}{2.5}$ [Each side is divided by 7.2]

$\frac{36}{7.5} = \frac{24}{5} = \frac{18}{3.7} .5$ [Each side is divided by 4.8]

$\frac{36}{10} = \frac{24}{6 \frac{2}{3}} = \frac{18}{5}$ [Each side is divided by 3.6]